In the field of signal processing methods are commonly used to transform data between different domains, for example, from the time domain to the frequency domain. One such equation that can be used to transform data is the Whittaker-Shannon-Kotelnikov (“WSK”) sampling theorem. The theorem describes two processes in signal processing, a sampling process in which a continuous time signal is converted into a discrete time signal, and a reconstruction process in which the original continuous time signal is recovered from the discrete signal. Reconstruction of the original continuous time signal is an interpolation process that mathematically defines a continuous-time signal from the discrete samples and times between the sample instants. During the interpolation process, unknown data values are approximated from surrounding known data values.
The WSK sampling theorem corresponds to Nyquist sampled data. The WSK sampling theorem provides a method for reconstructing a continuous time band-limited function from a discrete set of data points. The WSK sampling theorem assumes constant intervals between the data points. In other words, the theorem assumes a uniform data signal. Such a theorem is disadvantageous, however, when there is a need to reconstruct a non-uniform data signal. A need exists to overcome this deficiency.